Hoverboard

Sure. It's exactly the same as when you grab your bootstraps and lift your feet off the ground.

It is somewhat similar the the cat with a slice of buttered side up bread strapped to its back. Cats always land on their feet, and bread always lands buttered side down, so the cat just floats there.

Sorry, Sam. If the magnet is strong enough, you will compress the board.

Now, if the magnet is held on a hoist that isn't supported by the board, the board will rise, but it won't exactly float. It will be pulled all the way to the magnet.

Same as the bootstrap example. If someone else pulls your boot straps up hard enough, your feet will come off the ground.

Heres a lab experiment using the HALL EFFECT SENSOR that was developed at MIT for students of the trnsportation labs. It teaches you about what makes a MAglev train work (this is sorta what youre looking for
http://web.mit.edu/klund/www/papers/ACC04_maglev.pdf

but, if you have a floor that is a magnet and a board that is a magnet and turn them both so that their poles repel, the board, assuming it doesn't flip over, will hover, likely erratically though unless you place it in a denser environment, like custard or syrup maybe.
If you do fill your bedroom with syrup and attempt this, please write in to let me know how it went...